The superradiant instability of such a BH-condensate system is strongest when the boson's Compton wavelength is comparable to the BH radius, i.e. \(GM\mu /(\hbar c) \sim \mathcal {O}(1)\) , where \(M\)  and \(\mu \)  are the masses of the BH and the boson, respectively. The Standard Model particles are all too heavy, while many ultra-light beyond-Standard Model particles, such as QCD axion, axion-like particles suggested by string theory and dark photons could generate large superradiant instability around BHs with stellar mass or heavier [1]}, [2]}, [3]}, [4]}, [5]}. These bosons are also considered candidates for dark matter. Thus the studies of BH superradiance and their GW signals provide an independent strategy to restrict the mass range of these dark matter candidates.
